TY - JOUR

T1 - Analytical and monte carlo comparisons of six different linear least squares fits

AU - Jogesh Babu, Gutti

AU - Feigelson, Eric D.

N1 - Funding Information:
The authors would like to thank Dr. Marllyn Boswell (Penn State) for assistance with the numerical simulations, and Drs. Takashi Isobe (MIT) and Michael Akritas (Penn State) for their advice and assistance. Astronomical statistics at Penn State is sponsored by NASA grants NAGW-1917 and NAGW-2120, NSF grant DMS-9007717, and the Center of Excellence in Space Data and Information Sciences (operated by the Universities Space Research Association in cooperation with NASA). The authors would also like to thank the referees for helpful suggestions, which improved the presentation.

PY - 1992/1/1

Y1 - 1992/1/1

N2 - For many applications, particularly in allometry and astronomy, only a set of correlated data points (xi, yi) is available to fit a line.The underlying joint distribution is unknown, and it is not clear which variable is “dependent’ and which is “independent’.In such cases, the goal is an intrinsic functional relationship between the variables rather than E(Y|X), and the choice of leastsquares line is ambiguous.Astronomers and biometricians have used as many as six different linear regression methods for this situation: the two ordinary least-squares (OLS) lines, Pearson’s orthogonal regression, the OLS-bisector, the reduced major axis and the OLS-mean.The latter four methods treat the X and Y variables symmetrically.Series of simulations are described which compared the accuracy of regression estimators and their asymptotic variances for all six procedures.General relations between the regression slopes are also.

AB - For many applications, particularly in allometry and astronomy, only a set of correlated data points (xi, yi) is available to fit a line.The underlying joint distribution is unknown, and it is not clear which variable is “dependent’ and which is “independent’.In such cases, the goal is an intrinsic functional relationship between the variables rather than E(Y|X), and the choice of leastsquares line is ambiguous.Astronomers and biometricians have used as many as six different linear regression methods for this situation: the two ordinary least-squares (OLS) lines, Pearson’s orthogonal regression, the OLS-bisector, the reduced major axis and the OLS-mean.The latter four methods treat the X and Y variables symmetrically.Series of simulations are described which compared the accuracy of regression estimators and their asymptotic variances for all six procedures.General relations between the regression slopes are also.

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U2 - 10.1080/03610919208813034

DO - 10.1080/03610919208813034

M3 - Article

AN - SCOPUS:84903159033

SN - 0361-0918

VL - 21

SP - 533

EP - 549

JO - Communications in Statistics - Simulation and Computation

JF - Communications in Statistics - Simulation and Computation

IS - 2

ER -